When the positive integer N is divided by 16, the remainder is 3. Which of the following integers could be the remainder when N is divided by 6?

a. 0

b. 1

c. 2

d. 3

e. 4

f. 5

When the positive integer N is divided by 16, the remainder is 3. Which of the following integers could be the remainder when N is divided by 6?

a. 0

b. 1

c. 2

d. 3

e. 4

f. 5

Thus, N could be : 13,19,29,35,45,51,61,67,77,83,93,99 etc…

13 / 6 = 1 as remainder and if you continue u will find 1,3,4,5 as potential remainders of N

How did you get the various versions of N?

I just brute force the scenarios where the remainder is 3

6 × 1 = 16 | 16 × 6 = 96 |
---|---|

16 × 2 = 32 | 16 × 7 = 112 |

16 × 3 = 48 | 16 × 8 = 128 |

16 × 4 = 64 | 16 × 9 = 144 |

16 × 5 = 80 | 16 × 10 = 160 |

Now, to get a remainder as 3 ; you just ±3 from every multiple of 16.

For eg: first multiple of 16 is 16 (16x1 = 16) thus, 16-3 = 13 and 16+3 = 19 both when divided by 16 gives a remainder of 3

Ohhhh, I got it now. Thanks so much!!

Is it that N=45 divided by 16 equals 2 and the remainder is 13?, not 3